None.

Only if you look at recent statistics.
Western Buddhists entering Tibetan Vajrayana
as recently as the 1970's were experienced with
drugs.

Historically, no relationship.

Specifically regarding historical Zen, zero to none based on climate and ecology alone. More generally, (imo) enlightening states of being bear few experiential similarities to entheogenic states. Some would argue that MDMA as an empathogen would take one deeper into an enlightening state. A comparison of brainwave examples would confirm that there is little correlation, I believe.

This does not mean that entheogens cannot be valuable tools in a varaiety of works. It just means that there is probably no association between Zen, Chan, and potentially Buddhism in general on the one hand, and entheogens on the other.

Many, many people have used self medicated in order to access states of awareness that fall outside their normal perceptual field. This, in itself can be a powerful and inspiring experience.

"Medicines" can also be abused, either by being taken for granted and used recreationally and indiscriminately, or by being overused.

While their effects may provide dramatic though transitory shifts in attention, they are by no means a replacement for spiritual practice.

Imagine you are in a car driving down a long highway. There is a bunch of dirt and bugs spattered on your windshield. You have been driving for so long you don't notice the dirt, the bugs, or even the windshield--to you, the world *is* as it appears through your windshield.

Then imagine that your windshield suddenly turns purple. This is such a surprise, that you are suddenly reminded that you have been looking through a windshield, that there's a thick layer of dirt and bugs collected on it and that you can turn on your windshield washers to clear away some of the dirt, so you do. Now you can see better through the windshield except that everything's purple, but that's cool because you never noticed how different things looked when they were purple.

After a while the purple fades away. You are still aware that you are looking through the windshield and that it has already begun to accumulate a fresh layer of dirt (and bugs). At this point, you are in a precarious position. You know that by turning your windshield purple, you were able to notice things about the way you were looking through your windshield that you had forgotten. Observations which, even now, are fading.

So do you:

A) Continue to turn the windshield different colors. At least that way you stay aware of the windshield, the dirt the bugs, and... shit is that a chip?

B) Keep driving. You know the windshield isn't really purple. That was just because something turned it purple. Duh.

C) Jump out of the car. Fuck this!

D) Begin a practice of regularly cleaning the windshield, of regularly reminding yourself that you are looking through a windshield, and looking for practical ways of continuously improving the display quality afforded by your windshield, staying in the car until such a time as it seems safe to leave it, presumably after having arrived at a suitable destination?